1. Field of the Invention
The present invention relates generally to determining geological properties of subsurface formations using Nuclear Magnetic Resonance (“NMR”) methods for logging wellbores, particularly for correcting for the effects of tool motion on NMR signals.
2. Description of the Related Art
A variety of techniques are currently utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the wellbore drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the wellbore. Much of the logging is done after the well bores have been drilled. More recently, wellbores have been logged while drilling, which is referred to as measurement-while-drilling (MWD) or logging-while-drilling (LWD).
One commonly used technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things, porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the liquids in the geological formations surrounding the wellbore so that certain parameters such as nuclear spin density, longitudinal relaxation time (generally referred to in the art as T1) and transverse relaxation time (generally referred to as T2) of the geological formations can be measured. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
The NMR tools generate a static magnetic field in a region of interest surrounding the wellbore. NMR is based on the fact that the nuclei of many elements have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic Larmor resonant frequency related to the magnitude of the magnetic field in their locality. Over time the nuclear spins align themselves along an externally applied static magnetic field creating a net magnetization. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. The angle θ through which the spins exactly on resonance are tipped is given by the equation:θ=γB1tp/2  (1)where γ is the gyromagnetic ratio, B1 is the magnetic flux density amplitude of the sinusoidally oscillating field and tp is the duration of the RF pulse.
After tipping, the spins precess around the static field at a particular frequency known as the Larmor frequency ω0 given byω0=γB0  (2)where B0 is the static field strength. For hydrogen nuclei γ/2π=4258 Hz/Gauss, so that a static field of 235 Gauss, would produce a precession frequency of 1 MHz. At the same time, the magnetization returns to the equilibrium direction (i.e., aligned with the static field) according to a decay time known as the “spin-lattice relaxation time” or “longitudinal relaxation time” T1. T1 is controlled by the molecular environment and is typically ten to one thousand milliseconds in rocks.
At the end of a θ=90° tipping pulse, spins on resonance are pointed in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, because of inhomogeneities in the static field due to the constraints on tool shape, imperfect instrumentation, or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in phase and hence the NMR signal amplitude decays. This is known as the FID (free induction decay). This de-phasing occurs with a time constant that is commonly referred to as T2*. If the dephasing of spins is due to static magnetic field gradients then the dephasing can be reversed once or several times by one or more refocusing RF pulses that generate one or more spin echoes. The echo amplitude(s) decay with time constant T2, the “spin-spin relaxation time” or “transversal relaxation time”.
A receiving coil is designed so that a voltage is induced by the precessing spins. Only that magnetization that is perpendicular to the static magnetic field precesses around the static field and is sensed by the coil. After a 1800 tipping pulse (an “inversion pulse”), the spins on resonance are aligned opposite to the static field and the magnetization relaxes along the static field axis to the equilibrium direction. Hence, a signal will be generated after a 900 tipping pulse, but not after a 1800 tipping pulse in a generally uniform magnetic field.
While many different methods for measuring T1 have been developed, a single standard known as the CPMG sequence (Carr-Purcell-Meiboom-Gill) for measuring T2 has evolved. In contrast to laboratory NMR magnets, well logging tools have inhomogeneous magnetic fields due to the constraints on placing the magnets within a tubular tool and the inherent “inside-out” geometry. Maxwell's divergence theorem dictates that there cannot be a region of high homogeneity outside the tool. Therefore in typical well bores, T2*<<T2, and the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T2 in such situations, it is necessary to cancel the effect of the apparatus—and material-induced magnetic field inhomogeneities. To accomplish the same, a series of pulses is applied to repeatedly refocus the spin system, canceling the T2* effects and forming a series of spin echoes. The decay of echo amplitude is a true measure of the decay due to material properties. Furthermore it can be shown that the decay is in fact composed of a number of different decay components forming a T2 distribution. The echo decay data can be processed to reveal this distribution, which is related to rock pore size distribution and other parameters of interest to the well log analyst.
U.S. Pat. No. 5,023,551 issued to Kleinberg discloses an NMR pulse sequence for use in the borehole environment which combines a modified fast inversion recovery (FIR) pulse sequence with a series of more than ten, and typically hundreds, of CPMG pulses according to└Wi−180x−ti−90x−(tcp−180y−tcp−echo)j┘i  (3)where j=1, 2, . . . , J, and J is the number of echoes collected in a single CPMG sequence, where i=1, 2, . . . , I and I is the number of waiting times used in the pulse sequence, where Wi are the recovery times before the inversion pulse, and where ti are the recovery times before a CPMG sequence, and where tCP is the Carr-Purcell spacing. The phase of the RF pulses 90 and 180 is denoted by the subscripts X and Y, Y being phase shifted by π/2 radians with respect to X. The subscripts conventionally relate to the axis about which rotation of the magnetization occurs during the RF pulse in a local Cartesian coordinate system centered on the nucleus. Typically, the static magnetic field is aligned in the Z direction and the RF field in the X direction. This sequence can be used to measure both T1 and T2, but is very time consuming, limiting logging speed. If ti is set to zero and the inverting pulse is omitted then the sequence defaults to standard CPMG for measuring T2 only.
U.S. Pat. No. 6,466,013 to Hawkes et al., and U.S. Pat. No. 6,163,153 to Reiderman et al. teach use of a different NMR pulse-echo sequence in which the refocusing pulses have a tipping angle less than 1800. With such a sequence, power usage is reduced with no or at least no significant reduction in the signal to noise ratio (SNR). This pulse sequence may be referred to as an Optimized Rephasing Pulse Sequence (ORPS).
Tool motion can seriously affect the performance of NMR tools used in an MWD environment. NMR tools that have static and magnetic fields that have perfect axisymmetry are unaffected by rotation of the tool since the fields in the region of examination do not change during the measurement sequence. However, any radial or vertical component of tool motion, e.g. due to vibration will affect the NMR signal. U.S. Pat. No. 5,389,877 issued to Sezginer describes a truncated CPMG sequence in which the sequence duration and recovery delay are so short that only signals from the clay and capillary bound fluids are detected. A truncated sequence has the advantage that the effect of tool motion on the measurements is reduced due to the short measurement time (approx. 50 ms, compared to greater than 300 ms for normal downhole CPMG measurements.) As discussed in U.S. Pat. No. 5,705,927 issued to Kleinberg, resonance regions of many prior art instruments typically have a radial extent of the order of 1 mm. Accordingly, a lateral vibration having an amplitude of 1 mm would disable the instrument. The Kleinberg '927 patent discloses making the length of each CPMG sequence small, e.g. 10 ms, so that the drill collar cannot be displaced by a significant fraction of the vertical or radial extent of the sensitive region during a CPMG pulse sequence. However, as noted above, using such short sequences and short wait times only gives an indication of the bound fluid volume and, depending on the magnetization wait time, the total fluid volume (total porosity) but gives no indication of other fluid volumes.
U.S. Pat. No. 6,268,726 to Prammer et al. teaches the use of motion sensors on a MWD apparatus that makes measurements of tool motion of a NMR sensor assembly. Measurements are made by the NMR sensor during continued drilling operations, and subsequently, the measurements made by the motion sensor are used to select a subset of the NMR measurements that meet certain requirements on tool motion and hence would be expected to give a reasonable insensitivity to tool motion. U.S. Pat. No. 6,459,263 to Hawkes et al, having the same assignee as the present application and the contents of which are fully incorporated herein by reference, uses the output of motion sensors in combination with predictive filtering to control the timing of pulses for a conventional CPMG sequence, ORPS sequence, or other echo sequence. One drawback of the Hawkes '263 teaching is that merely choosing the best start time of the sequence does not fully compensate for the tool motion.
U.S. Pat. No. 6,051,973, to Prammer discusses a method for determining longitudinal relaxation times T1. In particular, the method comprises the steps of generating at least one radio frequency pulse covering a relatively wide range of frequencies to saturate the nuclear magnetization in a cylindrical volume around the tool; transmitting a readout pulse at a frequency near the center of the range of covered frequencies, the readout pulse following a predetermined wait time; applying at least one refocusing pulse following the readout pulse; receiving at least one NMR echo corresponding to the readout pulse; repeating the above steps for a different wait time to produce a plurality of data points a T1 relaxation curve; and processing the produced T1 relaxation curve to derive petrophysical properties of the formation.
UK Patent Application 2,346,216, of Speier et al, discusses a method of determining relative motion using two RF sequences. A first sequence has an envelope. The envelope is varied during the radiation of the first sequence to substantially saturate a first region of the sample. A second sequence of RF pulses is radiated to establish a resonance region with in the first region and measure an attribute of the sample.
U.S. Pat. No. 6,566,874 to Speier et al. addresses the problem of tool motion and teaches several approaches to dealing with the problem. In one embodiment, measurements are made of two different echo trains that have different sensitivities to tool motion. The tool has two different regions of examination: a high gradient zone defined by one set of magnets and antennas, and a low gradient zone defined by another set of magnets and antennas. The effect of tool motion on the signal amplitude is greater in the high gradient zone than in the low gradient zone. Using these two sets of signals and knowing the gradients of the respective zones, it is possible to estimate what the signal would have been without the tool motion. The Speier '874 patent also teaches that sensitivity to motion may be varied by different field geometries with different gradients. This requirement of having two different regions of examination complicates the hardware. Another drawback (noted in Speier '874) to the above-described techniques is that the measurements must be separated in time and/or space. In order to interpret the results it must be assumed that, in the absence of motion, the NMR signal (and therefore the formation properties measured) is the same in both measurements. For a continuously moving logging tool, this condition is not always given. Also the motion during the two measurements should be the same, or at least have the same characteristics.
In another embodiment taught by Speier '874, measurements are processed to obtain both the T1 and T2 distribution. The effect of tool motion is different on the two types of measurements. This approach has at least two drawbacks. The first is that T1 determination is time consuming. A second drawback is that in the absence of an exact knowledge of the ratio of T1/T2, the method can only be used for quality control and not for determining both the T1 and T2 distributions.
Another embodiment taught by Speier '874 analyzes the signal shape to give an indication of tool motion. Motion is simulated by altering the frequency of the RF signal. In the absence of a frequency shift, the imaginary component of the received echo signal is substantially zero. During a frequency shift of the RF pulse sequence, the imaginary component can be significant. Measurements made by two different filtering techniques are compared. In one, the signal amplitude in the absorption channel is taken at the echo maximum. This constitutes a broadband but noisy detection filter. In the second method, the normalized sum over all samples of the absorption signal is determined. By comparing the two measurements, motion effect can be identified.
Another embodiment taught by Speier '874 makes a comparison of measurements made in adjacent regions. The results derived from adjacent regions (by frequency shifting) are compared to give an indication of tool motion between the two acquisitions.
Yet another embodiment of Speier '874 attempts to address the problems caused by tool motion by preconditioning the spins to saturate a large region for a T1 based determination.
While the methods taught by Speier '874 are quite comprehensive, in one aspect the teachings of Speier '874 are incomplete. Specifically, the motion is simulated by altering the frequency of the RF signal. A better understanding of the effects of tool motion can be obtained by actually simulating movement of the tool with known magnetic field geometry. This is what is done in the present invention and leads to additional insights and additional methods of compensating for the effects of tool motion that are applicable to real world situations.